In order for democracy to survive and truly work we need to ensure that the electoral process is not tainted.
To answer you questions:
Deficit: I would argue that this could potentially reduce the deficit. First, I am not advocating we appropriate millions of dollars to each candidate. Second, I argue that this could potentially reduce the number of earmarks any given bill has (e.g. clearing a forest for a factory to be built, etc). Current legislation is riddled with pork barrel spending that is due to, in part, by the obligations that candidates have to special interests.
Who exactly would determine how much each candidate would receive? First, each candidate would receive the same, regardless of party and if future regulation is involved, I would suggest that all candidates should take part in debates. Second, the funds would be appropriated over time so only committed candidates would receive the full amount. Third, how much would each candidate receive? If more regulation is involved this would be easier to determine as it would be the amount to cover those costs. If candidates are limited they will use funds more efficiently as opposed to ridiculous attack ads (obama is a socialist, romney hates the middle class, etc)
Despite the influence of third party funds, I feel that primaries are generally fairly representative of the people and public funds can be used as opposed to taxpayer. While money from special interests would inevitably find its way in there, i think the effect is limited as opposed to special interests deciding final elections.
Lastly, would presidential campaigns get 6 billion dollars. Absolutely not.